Run download_data.Rmd and percentage_of_regional_richness.Rmd First!

library(randomForest)
randomForest 4.6-14
Type rfNews() to see new features/changes/bug fixes.
library(reshape2)
library(rpart)
library(ggplot2)

Attaching package: ‘ggplot2’

The following object is masked from ‘package:randomForest’:

    margin
library(tidyverse)
Registered S3 methods overwritten by 'dbplyr':
  method         from
  print.tbl_lazy     
  print.tbl_sql      
── Attaching packages ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── tidyverse 1.3.1 ──
✔ tibble  3.1.8     ✔ dplyr   1.0.7
✔ tidyr   1.1.3     ✔ stringr 1.4.0
✔ readr   1.4.0     ✔ forcats 0.5.1
✔ purrr   1.0.0     
Warning: package ‘tibble’ was built under R version 4.1.2Warning: package ‘purrr’ was built under R version 4.1.2── Conflicts ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── tidyverse_conflicts() ──
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✖ dplyr::filter()   masks stats::filter()
✖ dplyr::lag()      masks stats::lag()
✖ ggplot2::margin() masks randomForest::margin()
library(multcomp)
Loading required package: mvtnorm
Loading required package: survival
Loading required package: TH.data
Loading required package: MASS

Attaching package: ‘MASS’

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Attaching package: ‘TH.data’

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    geyser
library(car)
Loading required package: carData
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  method                          from
  influence.merMod                lme4
  cooks.distance.influence.merMod lme4
  dfbeta.influence.merMod         lme4
  dfbetas.influence.merMod        lme4

Attaching package: ‘car’

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library(VSURF)

library(boot)

Attaching package: ‘boot’

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    logit

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library(ggrepel)
city_data
length(city_data$city_gdp_per_population[!is.na(city_data$city_gdp_per_population)])
[1] 30
length(city_data$percentage_urban_area_as_open_public_spaces[!is.na(city_data$percentage_urban_area_as_open_public_spaces)])
[1] 61
length(city_data$happiness_future_life[!is.na(city_data$happiness_future_life)])
[1] 65
length(city_data$mean_population_exposure_to_pm2_5_2019[!is.na(city_data$mean_population_exposure_to_pm2_5_2019)])
[1] 131
fetch_city_data_for <- function(pool_name, include_city_name = F) {
  results_filename <- paste(paste('percentage_of_regional_richness__output_', pool_name, 'city', 'richness', 'intercept', sep = "_"), "csv", sep = ".")
  results <- read_csv(results_filename)
  
  joined <- left_join(city_data, results)
  joined$abs_city_centre_latitude = abs(joined$city_centre_latitude)
  
  required_columns <- c("population_growth", "rainfall_monthly_min", "rainfall_annual_average", "rainfall_monthly_max", "temperature_annual_average", "temperature_monthly_min", "temperature_monthly_max", "happiness_negative_effect", "happiness_positive_effect", "happiness_future_life", "number_of_biomes", "realm", "biome_name", "region_20km_includes_estuary", "region_50km_includes_estuary", "region_100km_includes_estuary", "city_includes_estuary", "region_20km_average_pop_density", "region_50km_average_pop_density", "region_100km_average_pop_density", "city_max_pop_density", "city_average_pop_density", "mean_population_exposure_to_pm2_5_2019", "region_20km_cultivated", "region_20km_urban", "region_50km_cultivated", "region_50km_urban", "region_100km_cultivated", "region_100km_urban", "region_20km_elevation_delta", "region_20km_mean_elevation", "region_50km_elevation_delta", "region_50km_mean_elevation", "region_100km_elevation_delta", "region_100km_mean_elevation", "city_elevation_delta", "city_mean_elevation", "urban", "shrubs", "permanent_water", "open_forest", "herbaceous_wetland", "herbaceous_vegetation", "cultivated", "closed_forest", "share_of_population_within_400m_of_open_space", "percentage_urban_area_as_streets", "percentage_urban_area_as_open_public_spaces_and_streets", "percentage_urban_area_as_open_public_spaces", "city_gdp_per_population", "city_ndvi", "city_ssm", "city_susm", "region_20km_ndvi", "region_20km_ssm", "region_20km_susm", "region_50km_ndvi", "region_50km_ssm", "region_50km_susm", "region_100km_ndvi", "region_100km_ssm", "region_100km_susm", "city_percentage_protected", "region_20km_percentage_protected", "region_50km_percentage_protected", "region_100km_percentage_protected", "city_centre_latitude", "abs_city_centre_latitude")
  
  if (include_city_name) {
    required_columns <- append(c("name"), required_columns)
  }
  
  required_columns <- append(c("response"), required_columns)
  
  joined[,required_columns]
}
Merlin Response
merlin_city_data <- fetch_city_data_for('merlin')

── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
cols(
  name = col_character(),
  response = col_double()
)
Joining, by = "name"
merlin_city_data
merlin_city_data_fixed <- rfImpute(response ~ ., merlin_city_data)
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    24.49   119.66 |
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    24.67   120.55 |
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    24.34   118.94 |
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    24.32   118.81 |
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    24.29   118.68 |
merlin_city_data_fixed
ggplot(merlin_city_data_fixed, aes(response)) + geom_histogram(binwidth = 2)

names(merlin_city_data_fixed)
 [1] "response"                                                "population_growth"                                       "rainfall_monthly_min"                                   
 [4] "rainfall_annual_average"                                 "rainfall_monthly_max"                                    "temperature_annual_average"                             
 [7] "temperature_monthly_min"                                 "temperature_monthly_max"                                 "happiness_negative_effect"                              
[10] "happiness_positive_effect"                               "happiness_future_life"                                   "number_of_biomes"                                       
[13] "realm"                                                   "biome_name"                                              "region_20km_includes_estuary"                           
[16] "region_50km_includes_estuary"                            "region_100km_includes_estuary"                           "city_includes_estuary"                                  
[19] "region_20km_average_pop_density"                         "region_50km_average_pop_density"                         "region_100km_average_pop_density"                       
[22] "city_max_pop_density"                                    "city_average_pop_density"                                "mean_population_exposure_to_pm2_5_2019"                 
[25] "region_20km_cultivated"                                  "region_20km_urban"                                       "region_50km_cultivated"                                 
[28] "region_50km_urban"                                       "region_100km_cultivated"                                 "region_100km_urban"                                     
[31] "region_20km_elevation_delta"                             "region_20km_mean_elevation"                              "region_50km_elevation_delta"                            
[34] "region_50km_mean_elevation"                              "region_100km_elevation_delta"                            "region_100km_mean_elevation"                            
[37] "city_elevation_delta"                                    "city_mean_elevation"                                     "urban"                                                  
[40] "shrubs"                                                  "permanent_water"                                         "open_forest"                                            
[43] "herbaceous_wetland"                                      "herbaceous_vegetation"                                   "cultivated"                                             
[46] "closed_forest"                                           "share_of_population_within_400m_of_open_space"           "percentage_urban_area_as_streets"                       
[49] "percentage_urban_area_as_open_public_spaces_and_streets" "percentage_urban_area_as_open_public_spaces"             "city_gdp_per_population"                                
[52] "city_ndvi"                                               "city_ssm"                                                "city_susm"                                              
[55] "region_20km_ndvi"                                        "region_20km_ssm"                                         "region_20km_susm"                                       
[58] "region_50km_ndvi"                                        "region_50km_ssm"                                         "region_50km_susm"                                       
[61] "region_100km_ndvi"                                       "region_100km_ssm"                                        "region_100km_susm"                                      
[64] "city_percentage_protected"                               "region_20km_percentage_protected"                        "region_50km_percentage_protected"                       
[67] "region_100km_percentage_protected"                       "city_centre_latitude"                                    "abs_city_centre_latitude"                               
merlin_response <- merlin_city_data_fixed$response
merlin_predictors <- merlin_city_data_fixed[,-1]
merlin_predictors
merlin_interp <- VSURF(x = merlin_predictors, y  = merlin_response)
Thresholding step
Estimated computational time (on one core): 116.5 sec.

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Interpretation step (on 45 variables)
Estimated computational time (on one core): between 58.5 sec. and  407.3 sec.

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Prediction step (on 4 variables)
Maximum estimated computational time (on one core): 5.2 sec.

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names(merlin_predictors[,merlin_interp$varselect.interp])
[1] "abs_city_centre_latitude"    "region_50km_elevation_delta" "region_50km_ssm"             "region_100km_ssm"           
Birdlife Response
birdlife_city_data <- fetch_city_data_for('birdlife')

── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
cols(
  name = col_character(),
  response = col_double()
)
Joining, by = "name"
birdlife_city_data
ggplot(birdlife_city_data, aes(response)) + geom_histogram(binwidth = 1)

birdlife_city_data_fixed <- rfImpute(response ~ ., birdlife_city_data)
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    5.695    90.15 |
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    5.688    90.04 |
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    5.602    88.68 |
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    5.824    92.20 |
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    5.771    91.36 |
birdlife_city_data_fixed
names(birdlife_city_data_fixed)
 [1] "response"                                                "population_growth"                                       "rainfall_monthly_min"                                   
 [4] "rainfall_annual_average"                                 "rainfall_monthly_max"                                    "temperature_annual_average"                             
 [7] "temperature_monthly_min"                                 "temperature_monthly_max"                                 "happiness_negative_effect"                              
[10] "happiness_positive_effect"                               "happiness_future_life"                                   "number_of_biomes"                                       
[13] "realm"                                                   "biome_name"                                              "region_20km_includes_estuary"                           
[16] "region_50km_includes_estuary"                            "region_100km_includes_estuary"                           "city_includes_estuary"                                  
[19] "region_20km_average_pop_density"                         "region_50km_average_pop_density"                         "region_100km_average_pop_density"                       
[22] "city_max_pop_density"                                    "city_average_pop_density"                                "mean_population_exposure_to_pm2_5_2019"                 
[25] "region_20km_cultivated"                                  "region_20km_urban"                                       "region_50km_cultivated"                                 
[28] "region_50km_urban"                                       "region_100km_cultivated"                                 "region_100km_urban"                                     
[31] "region_20km_elevation_delta"                             "region_20km_mean_elevation"                              "region_50km_elevation_delta"                            
[34] "region_50km_mean_elevation"                              "region_100km_elevation_delta"                            "region_100km_mean_elevation"                            
[37] "city_elevation_delta"                                    "city_mean_elevation"                                     "urban"                                                  
[40] "shrubs"                                                  "permanent_water"                                         "open_forest"                                            
[43] "herbaceous_wetland"                                      "herbaceous_vegetation"                                   "cultivated"                                             
[46] "closed_forest"                                           "share_of_population_within_400m_of_open_space"           "percentage_urban_area_as_streets"                       
[49] "percentage_urban_area_as_open_public_spaces_and_streets" "percentage_urban_area_as_open_public_spaces"             "city_gdp_per_population"                                
[52] "city_ndvi"                                               "city_ssm"                                                "city_susm"                                              
[55] "region_20km_ndvi"                                        "region_20km_ssm"                                         "region_20km_susm"                                       
[58] "region_50km_ndvi"                                        "region_50km_ssm"                                         "region_50km_susm"                                       
[61] "region_100km_ndvi"                                       "region_100km_ssm"                                        "region_100km_susm"                                      
[64] "city_percentage_protected"                               "region_20km_percentage_protected"                        "region_50km_percentage_protected"                       
[67] "region_100km_percentage_protected"                       "city_centre_latitude"                                    "abs_city_centre_latitude"                               
birdlife_response <- birdlife_city_data_fixed$response
birdlife_predictors <- birdlife_city_data_fixed[,-1]
birdlife_predictors
birdlife_interp <- VSURF(x = birdlife_predictors, y  = birdlife_response)
Thresholding step
Estimated computational time (on one core): 105.8 sec.

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Interpretation step (on 50 variables)
Estimated computational time (on one core): between 65 sec. and  432.5 sec.

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Prediction step (on 2 variables)
Maximum estimated computational time (on one core): 2.4 sec.

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names(birdlife_predictors[,birdlife_interp$varselect.interp])
[1] "population_growth" "region_50km_ssm"  
So….
Merlin: “abs_city_centre_latitude” “region_50km_elevation_delta” “region_50km_ssm” “region_100km_ssm” Birdlife: “population_growth” “region_50km_ssm”

Try Modelling

merlin_city_data_named <- fetch_city_data_for('merlin', T)

── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
cols(
  name = col_character(),
  response = col_double()
)
Joining, by = "name"
birdlife_city_data_named <- fetch_city_data_for('birdlife', T)

── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
cols(
  name = col_character(),
  response = col_double()
)
Joining, by = "name"
Use cross validation and dropping terms to find best model

full model: response ~ region_100km_ssm + region_20km_elevation_delta + region_20km_urban + region_100km_elevation_delta + temperature_annual_average + city_ndvi + city_gdp_per_population + shrubs + permanent_water + city_centre_latitude + region_20km_cultivated

Merlin data set

merlin_city_data_fixed_no_boreal <- merlin_city_data_fixed[merlin_city_data_fixed$biome_name != 'Boreal Forests/Taiga',]
cv.glm(merlin_city_data_fixed_no_boreal, glm(data = merlin_city_data_fixed_no_boreal, formula = response ~ abs_city_centre_latitude + region_50km_elevation_delta + region_50km_ssm + region_100km_ssm))$delta[1]
[1] 20.89733

– CVE 20.89733 – Can we drop one?

cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ abs_city_centre_latitude + region_50km_elevation_delta + region_50km_ssm, data = merlin_city_data_fixed_no_boreal))$delta[1]
[1] 20.62257
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ abs_city_centre_latitude + region_50km_elevation_delta + region_100km_ssm, data = merlin_city_data_fixed_no_boreal))$delta[1]
[1] 20.59091
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ abs_city_centre_latitude + region_50km_ssm + region_100km_ssm, data = merlin_city_data_fixed_no_boreal))$delta[1]
[1] 21.16605
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_elevation_delta + region_50km_ssm + region_100km_ssm, data = merlin_city_data_fixed_no_boreal))$delta[1]
[1] 20.65911

– drop region_50km_ssm to give smaller CVE of 20.59091 – can we drop another?

cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ abs_city_centre_latitude + region_50km_elevation_delta, data = merlin_city_data_fixed_no_boreal))$delta[1]
[1] 20.81971
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ abs_city_centre_latitude + region_100km_ssm, data = merlin_city_data_fixed_no_boreal))$delta[1]
[1] 20.85925
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_elevation_delta + region_100km_ssm, data = merlin_city_data_fixed_no_boreal))$delta[1]
[1] 20.34958

– drop abs_city_centre_latitude to give smaller CVE of 20.34958 – can we drop another?

cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_elevation_delta, data = merlin_city_data_fixed_no_boreal))$delta[1]
[1] 20.56209
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm, data = merlin_city_data_fixed_no_boreal))$delta[1]
[1] 20.62128

– No

– best model with region_100km_ssm + region_50km_elevation_delta (CV error 17.91216)
summary(glm(data = merlin_city_data_fixed, formula = response ~ region_100km_ssm + region_50km_elevation_delta))

Call:
glm(formula = response ~ region_100km_ssm + region_50km_elevation_delta, 
    data = merlin_city_data_fixed)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-7.7991  -3.2075  -0.5046   1.7160  18.6596  

Coefficients:
                              Estimate Std. Error t value Pr(>|t|)  
(Intercept)                  2.9334660  1.1943750   2.456   0.0153 *
region_100km_ssm            -0.1495523  0.0741115  -2.018   0.0456 *
region_50km_elevation_delta -0.0006995  0.0003687  -1.897   0.0600 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for gaussian family taken to be 19.70889)

    Null deviance: 2804  on 136  degrees of freedom
Residual deviance: 2641  on 134  degrees of freedom
AIC: 802.16

Number of Fisher Scoring iterations: 2
reg_merlin = glm(data = merlin_city_data_fixed, formula = response ~ region_100km_ssm + region_50km_elevation_delta)
with(summary(reg_merlin), 1 - deviance/null.deviance)
[1] 0.05815111

Birdlife data set

birdlife_city_data_fixed_no_boreal <- birdlife_city_data_fixed[birdlife_city_data_fixed$biome_name != 'Boreal Forests/Taiga',]
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ population_growth + region_50km_ssm, data = birdlife_city_data_fixed_no_boreal))$delta[1]
[1] 6.342024

– can we drop a variable?

cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]
[1] 6.464698
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm, data = birdlife_city_data_fixed_no_boreal))$delta[1]
[1] 6.291298

– drop population_growth to give CVE of 6.291298 – is this better than no variable?

cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ 1, data = birdlife_city_data_fixed_no_boreal))$delta[1]
[1] 6.3957

– yes

– so best model with birdlife is region_50km_ssm
summary(glm(data = birdlife_city_data_fixed, formula = response ~ region_50km_ssm))

Call:
glm(formula = response ~ region_50km_ssm, data = birdlife_city_data_fixed)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-4.5353  -1.5461  -0.4124   1.3071  10.7572  

Coefficients:
                Estimate Std. Error t value Pr(>|t|)  
(Intercept)      1.26916    0.65041   1.951   0.0531 .
region_50km_ssm -0.08499    0.04115  -2.065   0.0408 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for gaussian family taken to be 6.214378)

    Null deviance: 865.44  on 136  degrees of freedom
Residual deviance: 838.94  on 135  degrees of freedom
AIC: 643.05

Number of Fisher Scoring iterations: 2
reg_birdlife = glm(data = birdlife_city_data_fixed, formula = response ~ region_50km_ssm)
with(summary(reg_birdlife), 1 - deviance/null.deviance)
[1] 0.03062471
ggplot(birdlife_city_data_named, aes(x = region_50km_ssm, y = response)) + geom_point() + geom_smooth(method = "glm")

Check birdlife model fit
birdlife.fit <- glm(data = birdlife_city_data_fixed, formula = response ~ region_50km_ssm)
summary(birdlife.fit)

Call:
glm(formula = response ~ region_50km_ssm, data = birdlife_city_data_fixed)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-4.5353  -1.5461  -0.4124   1.3071  10.7572  

Coefficients:
                Estimate Std. Error t value Pr(>|t|)  
(Intercept)      1.26916    0.65041   1.951   0.0531 .
region_50km_ssm -0.08499    0.04115  -2.065   0.0408 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for gaussian family taken to be 6.214378)

    Null deviance: 865.44  on 136  degrees of freedom
Residual deviance: 838.94  on 135  degrees of freedom
AIC: 643.05

Number of Fisher Scoring iterations: 2
with(summary(birdlife.fit), 1 - deviance/null.deviance)
[1] 0.03062471
plot(birdlife.fit)

birdlife_city_data_fixed_no_boreal[c(16, 53, 72), c("region_50km_ssm")]
[1] 18.451180  9.961682 11.644862
city_data[c(16, 53, 72), c("name", "region_50km_ssm")]
dat <- predict(glm(formula = response ~ region_50km_ssm, data = birdlife_city_data_named), se.fit=T)

outside_se <- birdlife_city_data_named[birdlife_city_data_named$response < dat$fit - 15* dat$se.fit | birdlife_city_data_named$response > dat$fit + 15 * dat$se.fit,]

birdlife_ssm = ggplot(birdlife_city_data_named, aes(x = region_50km_ssm, y = response)) + 
  geom_point(size=1, alpha = 0.2) + 
  geom_smooth(method = "glm") +
  geom_text_repel(aes(label = name), data = outside_se, size = 3, nudge_y = 1, color = "red") +
  geom_point(data = outside_se, color = "red") +
  theme_bw() +
  ylab("Standardized response") + xlab("Regional (50km) SSM")

birdlife_ssm
ggsave("city_effect_richness__output__birdlife.jpg")
Saving 7.29 x 4.51 in image

How much variation have we explained?

birdlife_city_data_named$residuals <- resid(birdlife.fit)
ggplot(birdlife_city_data_named, aes(y = response, x = residuals)) + 
  geom_point() +
  geom_smooth(method = "lm", se = F) +
  labs(title = "Birdlife", subtitle = paste("Correlation", cor(birdlife_city_data_named$residuals, birdlife_city_data_named$response))) +
  theme_bw()

Check Merlin model fit
merlin.fit <- glm(data = merlin_city_data_named, formula = response ~ region_100km_ssm + region_50km_elevation_delta)
summary(merlin.fit)

Call:
glm(formula = response ~ region_100km_ssm + region_50km_elevation_delta, 
    data = merlin_city_data_named)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-7.7991  -3.2075  -0.5046   1.7160  18.6596  

Coefficients:
                              Estimate Std. Error t value Pr(>|t|)  
(Intercept)                  2.9334660  1.1943750   2.456   0.0153 *
region_100km_ssm            -0.1495523  0.0741115  -2.018   0.0456 *
region_50km_elevation_delta -0.0006995  0.0003687  -1.897   0.0600 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for gaussian family taken to be 19.70889)

    Null deviance: 2804  on 136  degrees of freedom
Residual deviance: 2641  on 134  degrees of freedom
AIC: 802.16

Number of Fisher Scoring iterations: 2
with(summary(merlin.fit), 1 - deviance/null.deviance)
[1] 0.05815111
plot(merlin.fit)

merlin_city_data_fixed_no_boreal[c(24, 42, 72), c("region_100km_ssm", "region_50km_elevation_delta")]
city_data[c(24, 42, 72), c("name", "region_100km_ssm", "region_50km_elevation_delta")]
ggplot(merlin_city_data_named, aes(x = region_100km_ssm, y = response)) + 
  geom_point(aes(size = region_50km_elevation_delta)) + 
  geom_smooth(method = "glm") +
  theme_bw() +
  theme(legend.position="bottom") +
  ylab("Standardized response") + xlab("SSM in 100 km surrounding city") + guides(size=guide_legend(title="Regional (50 km) elevation delta"))

ggsave("city_effect_richness__output__merlin.jpg")
Saving 7.29 x 4.51 in image

How much variation have we explained?

merlin_city_data_named$residuals <- resid(merlin.fit)
ggplot(merlin_city_data_named, aes(y = response, x = residuals)) + 
  geom_point() +
  geom_smooth(method = "lm", se = F) +
  labs(title = "Merlin", subtitle = paste("Correlation", cor(merlin_city_data_named$residuals, merlin_city_data_named$response))) +
  theme_bw()

Check AIC
AIC(
  glm(data = merlin_city_data_fixed, formula = response ~ region_100km_ssm + region_50km_ssm + region_50km_elevation_delta + biome_name + population_growth),
  glm(data = merlin_city_data_fixed, formula = response ~ region_100km_ssm + region_50km_elevation_delta)
)
AIC(
  glm(data = birdlife_city_data_fixed, formula = response ~ region_100km_ssm + region_50km_ssm + region_50km_elevation_delta + biome_name + population_growth),
  glm(data = birdlife_city_data_fixed, formula = response ~ region_50km_ssm)
)
LDG
birdlife_data_with_lat = fetch_city_data_for('birdlife', include_city_name = T)

── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
cols(
  name = col_character(),
  response = col_double()
)
Joining, by = "name"
model2 <- glm(formula = response ~ I(city_centre_latitude^2), data = birdlife_data_with_lat)
dat2 <- predict(model2, se.fit=T)
summary(model2)

Call:
glm(formula = response ~ I(city_centre_latitude^2), data = birdlife_data_with_lat)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-4.7461  -1.4878  -0.4638   1.2399   9.5839  

Coefficients:
                            Estimate Std. Error t value Pr(>|t|)  
(Intercept)               -0.4426687  0.3308024  -1.338   0.1831  
I(city_centre_latitude^2)  0.0004780  0.0002725   1.754   0.0817 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for gaussian family taken to be 6.267834)

    Null deviance: 865.44  on 136  degrees of freedom
Residual deviance: 846.16  on 135  degrees of freedom
AIC: 644.23

Number of Fisher Scoring iterations: 2
with(summary(model2), 1 - deviance/null.deviance)
[1] 0.02228615
outside_ldg_se <- birdlife_data_with_lat[birdlife_data_with_lat$response < dat2$fit - 15* dat2$se.fit | birdlife_data_with_lat$response > dat2$fit + 15 * dat2$se.fit,]

birdlife_ldg = ggplot(birdlife_data_with_lat, aes(x = city_centre_latitude, y = response)) + 
  geom_point(size=1, alpha = 0.2) + 
  geom_smooth(method = "glm", formula = y ~ I(x^2)) +
  geom_text_repel(aes(label = name), data = outside_ldg_se, size = 3, nudge_y = 1, color = "red") +
  geom_point(data = outside_ldg_se, color = "red") +
  theme_bw() +
  ylab("Standardized response") + xlab("Latitude (of city centre)") + labs(title = "Birdlife LDG")

birdlife_ldg
ggsave('city_effect_richness__output__ldg_birdlife.jpg')
Saving 7.29 x 4.51 in image

library(grid)
library(gridExtra)

Attaching package: ‘gridExtra’

The following object is masked from ‘package:dplyr’:

    combine

The following object is masked from ‘package:randomForest’:

    combine
birdlife_plot_ldg = ggplot(birdlife_data_with_lat, aes(x = city_centre_latitude, y = response)) + 
  geom_point(size=1, alpha = 0.2) + 
  geom_smooth(method = "glm", formula = y ~ I(x^2)) +
  geom_text_repel(aes(label = name), data = outside_ldg_se, size = 3, nudge_y = 1, color = "red") +
  geom_point(data = outside_ldg_se, aes(color = region_50km_ssm)) +
  scale_colour_gradientn(colours = c("#ffee00", "#0019ff"), limits=c(5,22)) +
  guides(colour=guide_legend(title="SSM in 50 km surrounding city")) +
  theme_bw() +
  ylab("Standardized response") + xlab("Latitude (of city centre)") + 
  theme(legend.position="bottom", legend.box = "horizontal")

birdlife_plot_ldg

outside_ssm_se <- birdlife_city_data_named[birdlife_city_data_named$response < dat$fit - 15* dat$se.fit | birdlife_city_data_named$response > dat$fit + 15 * dat$se.fit,]

birdlife_ssm2 = ggplot(birdlife_city_data_named, aes(x = region_50km_ssm, y = response)) + 
  geom_point(size=1, alpha = 0.2) + 
  geom_smooth(method = "glm") +
  geom_text_repel(aes(label = name), data = outside_ssm_se, size = 3, nudge_y = 1, color = "red") +
  geom_point(data = outside_ssm_se, aes(color = region_50km_ssm)) +
  scale_colour_gradientn(colours = c("#ffee00", "#0019ff"), limits=c(5,22)) +
  guides(colour=guide_legend(title="SSM in 50 km surrounding city")) +
  theme_bw() +
  ylab("Standardized response") + xlab("SSM in 50 km surrounding city") +
  theme(legend.position="bottom", legend.box = "horizontal")

birdlife_ssm2

library(ggpubr)
birdlife_figure = ggarrange(birdlife_ssm2 + rremove("ylab"), birdlife_plot_ldg + rremove("ylab"), labels = c("a", "b"), ncol = 2, common.legend = T, legend = "bottom")
`geom_smooth()` using formula 'y ~ x'
`geom_smooth()` using formula 'y ~ x'
annotate_figure(birdlife_figure,
                left = text_grob("Standardized response", rot = 90))


ggsave('city_effect_richness__output__ldg_birdlife_with_ssm.jpg', height = 1500, width = 2250, units = "px")

merlin_data_with_lat = fetch_city_data_for('merlin', include_city_name = T)

── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
cols(
  name = col_character(),
  response = col_double()
)
Joining, by = "name"
model2 <- glm(formula = response ~ I(city_centre_latitude^2), data = merlin_data_with_lat)
dat2 <- predict(model2, se.fit=T)
summary(model2)

Call:
glm(formula = response ~ I(city_centre_latitude^2), data = merlin_data_with_lat)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-9.7067  -3.1557  -0.3365   1.4217  20.3506  

Coefficients:
                            Estimate Std. Error t value Pr(>|t|)
(Intercept)                6.972e-02  6.021e-01   0.116    0.908
I(city_centre_latitude^2) -7.529e-05  4.960e-04  -0.152    0.880

(Dispersion parameter for gaussian family taken to be 20.76719)

    Null deviance: 2804.0  on 136  degrees of freedom
Residual deviance: 2803.6  on 135  degrees of freedom
AIC: 808.35

Number of Fisher Scoring iterations: 2
with(summary(model2), 1 - deviance/null.deviance)
[1] 0.0001706366
outside_se <- merlin_data_with_lat[merlin_data_with_lat$response < dat2$fit - 15* dat2$se.fit | merlin_data_with_lat$response > dat2$fit + 15 * dat2$se.fit,]

ggplot(merlin_data_with_lat, aes(x = city_centre_latitude, y = response)) + 
  geom_point(size=1, alpha = 0.2) + 
  geom_smooth(method = "glm", formula = y ~ I(x^2)) +
  geom_text_repel(aes(label = name), data = outside_se, size = 3, nudge_y = 1, color = "red") +
  geom_point(data = outside_se, color = "red") +
  theme_bw() +
  ylab("Standardized response") + xlab("Latitude (of city centre)")

ggsave('city_effect_richness__output__ldg_merlin.jpg')
Saving 7.29 x 4.51 in image

---
title: "R Notebook"
output: html_notebook
---
Run `download_data.Rmd` and `percentage_of_regional_richness.Rmd` First!

```{r setup}
library(randomForest)
library(reshape2)
library(rpart)
library(ggplot2)
library(tidyverse)

library(multcomp)
library(car)
library(VSURF)

library(boot)

library(ggrepel)
```

```{r}
city_data
```

```{r}
length(city_data$city_gdp_per_population[!is.na(city_data$city_gdp_per_population)])
length(city_data$percentage_urban_area_as_open_public_spaces[!is.na(city_data$percentage_urban_area_as_open_public_spaces)])
length(city_data$happiness_future_life[!is.na(city_data$happiness_future_life)])
length(city_data$mean_population_exposure_to_pm2_5_2019[!is.na(city_data$mean_population_exposure_to_pm2_5_2019)])
```

```{r}
fetch_city_data_for <- function(pool_name, include_city_name = F) {
  results_filename <- paste(paste('percentage_of_regional_richness__output_', pool_name, 'city', 'richness', 'intercept', sep = "_"), "csv", sep = ".")
  results <- read_csv(results_filename)
  
  joined <- left_join(city_data, results)
  joined$abs_city_centre_latitude = abs(joined$city_centre_latitude)
  
  required_columns <- c("population_growth", "rainfall_monthly_min", "rainfall_annual_average", "rainfall_monthly_max", "temperature_annual_average", "temperature_monthly_min", "temperature_monthly_max", "happiness_negative_effect", "happiness_positive_effect", "happiness_future_life", "number_of_biomes", "realm", "biome_name", "region_20km_includes_estuary", "region_50km_includes_estuary", "region_100km_includes_estuary", "city_includes_estuary", "region_20km_average_pop_density", "region_50km_average_pop_density", "region_100km_average_pop_density", "city_max_pop_density", "city_average_pop_density", "mean_population_exposure_to_pm2_5_2019", "region_20km_cultivated", "region_20km_urban", "region_50km_cultivated", "region_50km_urban", "region_100km_cultivated", "region_100km_urban", "region_20km_elevation_delta", "region_20km_mean_elevation", "region_50km_elevation_delta", "region_50km_mean_elevation", "region_100km_elevation_delta", "region_100km_mean_elevation", "city_elevation_delta", "city_mean_elevation", "urban", "shrubs", "permanent_water", "open_forest", "herbaceous_wetland", "herbaceous_vegetation", "cultivated", "closed_forest", "share_of_population_within_400m_of_open_space", "percentage_urban_area_as_streets", "percentage_urban_area_as_open_public_spaces_and_streets", "percentage_urban_area_as_open_public_spaces", "city_gdp_per_population", "city_ndvi", "city_ssm", "city_susm", "region_20km_ndvi", "region_20km_ssm", "region_20km_susm", "region_50km_ndvi", "region_50km_ssm", "region_50km_susm", "region_100km_ndvi", "region_100km_ssm", "region_100km_susm", "city_percentage_protected", "region_20km_percentage_protected", "region_50km_percentage_protected", "region_100km_percentage_protected", "city_centre_latitude", "abs_city_centre_latitude")
  
  if (include_city_name) {
    required_columns <- append(c("name"), required_columns)
  }
  
  required_columns <- append(c("response"), required_columns)
  
  joined[,required_columns]
}
```


----------------------
Merlin Response
----------------------

```{r}
merlin_city_data <- fetch_city_data_for('merlin')
merlin_city_data
```

```{r}
merlin_city_data_fixed <- rfImpute(response ~ ., merlin_city_data)
merlin_city_data_fixed
```

```{r}
ggplot(merlin_city_data_fixed, aes(response)) + geom_histogram(binwidth = 2)
```

```{r}
names(merlin_city_data_fixed)
```

```{r}
merlin_response <- merlin_city_data_fixed$response
merlin_predictors <- merlin_city_data_fixed[,-1]
merlin_predictors
```

```{r, cache = TRUE}
merlin_interp <- VSURF(x = merlin_predictors, y  = merlin_response)
```

```{r}
names(merlin_predictors[,merlin_interp$varselect.interp])
```

----------------------
Birdlife Response
----------------------
```{r}
birdlife_city_data <- fetch_city_data_for('birdlife')
birdlife_city_data
```



```{r}
ggplot(birdlife_city_data, aes(response)) + geom_histogram(binwidth = 1)
```

```{r}
birdlife_city_data_fixed <- rfImpute(response ~ ., birdlife_city_data)
birdlife_city_data_fixed
```

```{r}
names(birdlife_city_data_fixed)
```

```{r}
birdlife_response <- birdlife_city_data_fixed$response
birdlife_predictors <- birdlife_city_data_fixed[,-1]
birdlife_predictors
```


```{r, cache = TRUE}
birdlife_interp <- VSURF(x = birdlife_predictors, y  = birdlife_response)
```

```{r}
names(birdlife_predictors[,birdlife_interp$varselect.interp])
```


------------------------------------------
So....
------------------------------------------
Merlin: "abs_city_centre_latitude"    "region_50km_elevation_delta" "region_50km_ssm"             "region_100km_ssm" 
Birdlife: "population_growth" "region_50km_ssm"  

-----------------------------
Try Modelling
-----------------------------


```{r}
merlin_city_data_named <- fetch_city_data_for('merlin', T)
birdlife_city_data_named <- fetch_city_data_for('birdlife', T)
```

------------------------------------------------------------------
Use cross validation and dropping terms to find best model
------------------------------------------------------------------

full model:  response ~ region_100km_ssm + region_20km_elevation_delta + region_20km_urban + region_100km_elevation_delta + temperature_annual_average + city_ndvi + city_gdp_per_population + shrubs + permanent_water + city_centre_latitude + region_20km_cultivated


Merlin data set
----------------
```{r}
merlin_city_data_fixed_no_boreal <- merlin_city_data_fixed[merlin_city_data_fixed$biome_name != 'Boreal Forests/Taiga',]
```

```{r}
cv.glm(merlin_city_data_fixed_no_boreal, glm(data = merlin_city_data_fixed_no_boreal, formula = response ~ abs_city_centre_latitude + region_50km_elevation_delta + region_50km_ssm + region_100km_ssm))$delta[1]
```

-- CVE 20.89733
-- Can we drop one?

```{r}
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ abs_city_centre_latitude + region_50km_elevation_delta + region_50km_ssm, data = merlin_city_data_fixed_no_boreal))$delta[1]
```

```{r}
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ abs_city_centre_latitude + region_50km_elevation_delta + region_100km_ssm, data = merlin_city_data_fixed_no_boreal))$delta[1]
```

```{r}
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ abs_city_centre_latitude + region_50km_ssm + region_100km_ssm, data = merlin_city_data_fixed_no_boreal))$delta[1]
```

```{r}
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_elevation_delta + region_50km_ssm + region_100km_ssm, data = merlin_city_data_fixed_no_boreal))$delta[1]
```


-- drop region_50km_ssm to give smaller CVE of 20.59091
-- can we drop another?

```{r}
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ abs_city_centre_latitude + region_50km_elevation_delta, data = merlin_city_data_fixed_no_boreal))$delta[1]
```

```{r}
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ abs_city_centre_latitude + region_100km_ssm, data = merlin_city_data_fixed_no_boreal))$delta[1]
```

```{r}
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_elevation_delta + region_100km_ssm, data = merlin_city_data_fixed_no_boreal))$delta[1]
```

-- drop abs_city_centre_latitude to give smaller CVE of 20.34958
-- can we drop another?

```{r}
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_elevation_delta, data = merlin_city_data_fixed_no_boreal))$delta[1]
```

```{r}
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm, data = merlin_city_data_fixed_no_boreal))$delta[1]
```

-- No

----------------------------------------------------------------------------------------------
-- best model with region_100km_ssm + region_50km_elevation_delta (CV error 17.91216)
----------------------------------------------------------------------------------------------

```{r}
summary(glm(data = merlin_city_data_fixed, formula = response ~ region_100km_ssm + region_50km_elevation_delta))
```

```{r}
reg_merlin = glm(data = merlin_city_data_fixed, formula = response ~ region_100km_ssm + region_50km_elevation_delta)
with(summary(reg_merlin), 1 - deviance/null.deviance)
```

Birdlife data set
----------------
```{r}
birdlife_city_data_fixed_no_boreal <- birdlife_city_data_fixed[birdlife_city_data_fixed$biome_name != 'Boreal Forests/Taiga',]
```

```{r}
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ population_growth + region_50km_ssm, data = birdlife_city_data_fixed_no_boreal))$delta[1]
```

-- can we drop a variable?

```{r}
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]
```

```{r}
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm, data = birdlife_city_data_fixed_no_boreal))$delta[1]
```


-- drop population_growth to give CVE of 6.291298
-- is this better than no variable?

```{r}
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ 1, data = birdlife_city_data_fixed_no_boreal))$delta[1]
```
-- yes

----------------------------------------------------
-- so best model with birdlife is region_50km_ssm
----------------------------------------------------

```{r}
summary(glm(data = birdlife_city_data_fixed, formula = response ~ region_50km_ssm))
```

```{r}
reg_birdlife = glm(data = birdlife_city_data_fixed, formula = response ~ region_50km_ssm)
with(summary(reg_birdlife), 1 - deviance/null.deviance)
```


```{r}
ggplot(birdlife_city_data_named, aes(x = region_50km_ssm, y = response)) + geom_point() + geom_smooth(method = "glm")
```



------------------------
Check birdlife model fit
------------------------

```{r}
birdlife.fit <- glm(data = birdlife_city_data_fixed, formula = response ~ region_50km_ssm)
summary(birdlife.fit)
with(summary(birdlife.fit), 1 - deviance/null.deviance)
plot(birdlife.fit)
```

```{r}
birdlife_city_data_fixed_no_boreal[c(16, 53, 72), c("region_50km_ssm")]
```

```{r}
city_data[c(16, 53, 72), c("name", "region_50km_ssm")]
```

```{r}
dat <- predict(glm(formula = response ~ region_50km_ssm, data = birdlife_city_data_named), se.fit=T)

outside_se <- birdlife_city_data_named[birdlife_city_data_named$response < dat$fit - 15* dat$se.fit | birdlife_city_data_named$response > dat$fit + 15 * dat$se.fit,]

birdlife_ssm = ggplot(birdlife_city_data_named, aes(x = region_50km_ssm, y = response)) + 
  geom_point(size=1, alpha = 0.2) + 
  geom_smooth(method = "glm") +
  geom_text_repel(aes(label = name), data = outside_se, size = 3, nudge_y = 1, color = "red") +
  geom_point(data = outside_se, color = "red") +
  theme_bw() +
  ylab("Standardized response") + xlab("Regional (50km) SSM")

birdlife_ssm
ggsave("city_effect_richness__output__birdlife.jpg")
```

How much variation have we explained?
------------------------------------

```{r}
birdlife_city_data_named$residuals <- resid(birdlife.fit)
ggplot(birdlife_city_data_named, aes(y = response, x = residuals)) + 
  geom_point() +
  geom_smooth(method = "lm", se = F) +
  labs(title = "Birdlife", subtitle = paste("Correlation", cor(birdlife_city_data_named$residuals, birdlife_city_data_named$response))) +
  theme_bw()
```

------------------------
Check Merlin model fit
------------------------

```{r}
merlin.fit <- glm(data = merlin_city_data_named, formula = response ~ region_100km_ssm + region_50km_elevation_delta)
summary(merlin.fit)
with(summary(merlin.fit), 1 - deviance/null.deviance)
plot(merlin.fit)
```

```{r}
merlin_city_data_fixed_no_boreal[c(24, 42, 72), c("region_100km_ssm", "region_50km_elevation_delta")]
```

```{r}
city_data[c(24, 42, 72), c("name", "region_100km_ssm", "region_50km_elevation_delta")]
```

```{r}
ggplot(merlin_city_data_named, aes(x = region_100km_ssm, y = response)) + 
  geom_point(aes(size = region_50km_elevation_delta)) + 
  geom_smooth(method = "glm") +
  theme_bw() +
  theme(legend.position="bottom") +
  ylab("Standardized response") + xlab("SSM in 100 km surrounding city") + guides(size=guide_legend(title="Regional (50 km) elevation delta"))

ggsave("city_effect_richness__output__merlin.jpg")
```

How much variation have we explained?
------------------------------------
```{r}
merlin_city_data_named$residuals <- resid(merlin.fit)
ggplot(merlin_city_data_named, aes(y = response, x = residuals)) + 
  geom_point() +
  geom_smooth(method = "lm", se = F) +
  labs(title = "Merlin", subtitle = paste("Correlation", cor(merlin_city_data_named$residuals, merlin_city_data_named$response))) +
  theme_bw()
```


-------------------------
Check AIC
-------------------------

```{r}
AIC(
  glm(data = merlin_city_data_fixed, formula = response ~ region_100km_ssm + region_50km_ssm + region_50km_elevation_delta + biome_name + population_growth),
  glm(data = merlin_city_data_fixed, formula = response ~ region_100km_ssm + region_50km_elevation_delta)
)
```

```{r}
AIC(
  glm(data = birdlife_city_data_fixed, formula = response ~ region_100km_ssm + region_50km_ssm + region_50km_elevation_delta + biome_name + population_growth),
  glm(data = birdlife_city_data_fixed, formula = response ~ region_50km_ssm)
)
```



---------------------
LDG
----------------------
```{r}
birdlife_data_with_lat = fetch_city_data_for('birdlife', include_city_name = T)

model2 <- glm(formula = response ~ I(city_centre_latitude^2), data = birdlife_data_with_lat)
dat2 <- predict(model2, se.fit=T)
summary(model2)

with(summary(model2), 1 - deviance/null.deviance)

outside_ldg_se <- birdlife_data_with_lat[birdlife_data_with_lat$response < dat2$fit - 15* dat2$se.fit | birdlife_data_with_lat$response > dat2$fit + 15 * dat2$se.fit,]

birdlife_ldg = ggplot(birdlife_data_with_lat, aes(x = city_centre_latitude, y = response)) + 
  geom_point(size=1, alpha = 0.2) + 
  geom_smooth(method = "glm", formula = y ~ I(x^2)) +
  geom_text_repel(aes(label = name), data = outside_ldg_se, size = 3, nudge_y = 1, color = "red") +
  geom_point(data = outside_ldg_se, color = "red") +
  theme_bw() +
  ylab("Standardized response") + xlab("Latitude (of city centre)") + labs(title = "Birdlife LDG")

birdlife_ldg
ggsave('city_effect_richness__output__ldg_birdlife.jpg')
```


```{r}
library(grid)
library(gridExtra)
birdlife_plot_ldg = ggplot(birdlife_data_with_lat, aes(x = city_centre_latitude, y = response)) + 
  geom_point(size=1, alpha = 0.2) + 
  geom_smooth(method = "glm", formula = y ~ I(x^2)) +
  geom_text_repel(aes(label = name), data = outside_ldg_se, size = 3, nudge_y = 1, color = "red") +
  geom_point(data = outside_ldg_se, aes(color = region_50km_ssm)) +
  scale_colour_gradientn(colours = c("#ffee00", "#0019ff"), limits=c(5,22)) +
  guides(colour=guide_legend(title="SSM in 50 km surrounding city")) +
  theme_bw() +
  ylab("Standardized response") + xlab("Latitude (of city centre)") + 
  theme(legend.position="bottom", legend.box = "horizontal")

birdlife_plot_ldg
```
```{r}
outside_ssm_se <- birdlife_city_data_named[birdlife_city_data_named$response < dat$fit - 15* dat$se.fit | birdlife_city_data_named$response > dat$fit + 15 * dat$se.fit,]

birdlife_ssm2 = ggplot(birdlife_city_data_named, aes(x = region_50km_ssm, y = response)) + 
  geom_point(size=1, alpha = 0.2) + 
  geom_smooth(method = "glm") +
  geom_text_repel(aes(label = name), data = outside_ssm_se, size = 3, nudge_y = 1, color = "red") +
  geom_point(data = outside_ssm_se, aes(color = region_50km_ssm)) +
  scale_colour_gradientn(colours = c("#ffee00", "#0019ff"), limits=c(5,22)) +
  guides(colour=guide_legend(title="SSM in 50 km surrounding city")) +
  theme_bw() +
  ylab("Standardized response") + xlab("SSM in 50 km surrounding city") +
  theme(legend.position="bottom", legend.box = "horizontal")

birdlife_ssm2
```

```{r}
library(ggpubr)
birdlife_figure = ggarrange(birdlife_ssm2 + rremove("ylab"), birdlife_plot_ldg + rremove("ylab"), labels = c("a", "b"), ncol = 2, common.legend = T, legend = "bottom")
annotate_figure(birdlife_figure,
                left = text_grob("Standardized response", rot = 90))

ggsave('city_effect_richness__output__ldg_birdlife_with_ssm.jpg', height = 1500, width = 2250, units = "px")
```

```{r}
merlin_data_with_lat = fetch_city_data_for('merlin', include_city_name = T)

model2 <- glm(formula = response ~ I(city_centre_latitude^2), data = merlin_data_with_lat)
dat2 <- predict(model2, se.fit=T)
summary(model2)

with(summary(model2), 1 - deviance/null.deviance)

outside_se <- merlin_data_with_lat[merlin_data_with_lat$response < dat2$fit - 15* dat2$se.fit | merlin_data_with_lat$response > dat2$fit + 15 * dat2$se.fit,]

ggplot(merlin_data_with_lat, aes(x = city_centre_latitude, y = response)) + 
  geom_point(size=1, alpha = 0.2) + 
  geom_smooth(method = "glm", formula = y ~ I(x^2)) +
  geom_text_repel(aes(label = name), data = outside_se, size = 3, nudge_y = 1, color = "red") +
  geom_point(data = outside_se, color = "red") +
  theme_bw() +
  ylab("Standardized response") + xlab("Latitude (of city centre)")

ggsave('city_effect_richness__output__ldg_merlin.jpg')
```